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(c) 2001 Contemporary Engineering Economics 2 Rate of Return Definition: A relative percentage method which measures the annual rate of return as a percentage of investment over the life of a project Example: Vincent Gogh’s painting John Whitney Payson bought the art at $80,000. John sold the art at $53.9 million in 40 years. What is the rate of return on John’s investment?

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(c) 2001 Contemporary Engineering Economics 4 In 1970, when Wal-Mart Stores, Inc. went public, an investment of 100 shares cost $1,650. That investment would have been worth $13,312,000 on January 31, 2000. What is the rate of return on that investment? Meaning of Rate of Return

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(c) 2001 Contemporary Engineering Economics 6 So, in 1970, as long as you earn more than 6% interest in another investment, you will take that investment. Therefore, that 6% is viewed as a minimum attractive rate of return (or required rate of return). So, you can apply the following decision rule, to see if the proposed investment is a good one. ROR > MARR

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(c) 2001 Contemporary Engineering Economics 7 Return on Investment Definition 1: Rate of return (ROR) is defined as the interest rate earned on the unpaid balance of an installment loan. Example: A bank lends $10,000 and receives annual payment of $4,021 over 3 years. The bank is said to earn a return of 10% on its loan of $10,000.

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(c) 2001 Contemporary Engineering Economics 9 Rate of Return: Definition 2: Rate of return (ROR) is the break-even interest rate, i *, which equates the present worth of a project’s cash outflows to the present worth of its cash inflows. Mathematical Relation:

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(c) 2001 Contemporary Engineering Economics 10 Return on Invested Capital Definition 3: Return on invested capital is the interest rate charged on the unrecovered project balance of the investment project. It is commonly known as internal rate of return (IRR). Example: A company invests $10,000 in a computer and results in equivalent annual labor savings of $4,021 over 3 years. The company is said to earn a return of 10% on its investment of $10,000.

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(c) 2001 Contemporary Engineering Economics 20 Incremental Investment Assuming MARR of 10%, you can always earn that rate from other investment source, i.e., $4,400 at the end of one year for $4,000 investment. By investing the additional $4,000 in A2, you would make additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the incremental investment in A2 is justified. nProject A1Project A2 Incremental Investment (A2 – A1) 0101 -$1,000 $2,000 -$5,000 $7,000 -$4,000 $5,000 ROR PW(10%) 100% $818 40% $1,364 25% $546

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(c) 2001 Contemporary Engineering Economics 21 Incremental Analysis (Procedure) Step 1:Compute the cash flows for the difference between the projects (A,B) by subtracting the cash flows for the lower investment cost project (A) from those of the higher investment cost project (B). Step 2:Compute the IRR on this incremental investment (IRR ). Step 3:Accept the investment B if and only if IRR B-A > MARR B-A